fenl_functors.hpp
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fenl_functors.hpp
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			#ifndef KOKKOS_EXAMPLE_FENLFUNCTORS_HPP
			#define KOKKOS_EXAMPLE_FENLFUNCTORS_HPP

			#include <cstdio>

			#include <iostream>
			#include <fstream>
			#include <iomanip>
			#include <cstdlib>
			#include <cmath>
			#include <limits>

			#include <Kokkos_Pair.hpp>
			#include <Kokkos_UnorderedMap.hpp>

			#include <impl/Kokkos_Timer.hpp>

			#include <BoxElemFixture.hpp>
			#include <HexElement.hpp>
			#include <CGSolve.hpp>

			//----------------------------------------------------------------------------
			//----------------------------------------------------------------------------

			namespace Kokkos {
			namespace Example {
			namespace FENL {

			template< class ElemNodeIdView , class CrsGraphType , unsigned ElemNode >
			class NodeNodeGraph {
			public:

			typedef typename ElemNodeIdView::execution_space execution_space ;
			typedef pair<unsigned,unsigned> key_type ;

			typedef Kokkos::UnorderedMap< key_type, void , execution_space > SetType ;
			typedef typename CrsGraphType::row_map_type::non_const_type RowMapType ;
			typedef Kokkos::View< unsigned , execution_space > UnsignedValue ;

			// Static dimensions of 0 generate compiler warnings or errors.
			typedef Kokkos::View< unsigned*[ElemNode][ElemNode] , execution_space >
			ElemGraphType ;

			struct TagFillNodeSet {};
			struct TagScanNodeCount {};
			struct TagFillGraphEntries {};
			struct TagSortGraphEntries {};
			struct TagFillElementGraph {};

			private:

			enum PhaseType { FILL_NODE_SET ,
			SCAN_NODE_COUNT ,
			FILL_GRAPH_ENTRIES ,
			SORT_GRAPH_ENTRIES ,
			FILL_ELEMENT_GRAPH };

			const unsigned node_count ;
			const ElemNodeIdView elem_node_id ;
			UnsignedValue row_total ;
			RowMapType row_count ;
			RowMapType row_map ;
			SetType node_node_set ;
			PhaseType phase ;

			public:

			CrsGraphType graph ;
			ElemGraphType elem_graph ;

			struct Times
			{
			double ratio;
			double fill_node_set;
			double scan_node_count;
			double fill_graph_entries;
			double sort_graph_entries;
			double fill_element_graph;
			};

			NodeNodeGraph( const ElemNodeIdView & arg_elem_node_id ,
			const unsigned arg_node_count,
			Times & results
			)
			: node_count(arg_node_count)
			, elem_node_id( arg_elem_node_id )
			, row_total( "row_total" )
			, row_count(Kokkos::ViewAllocateWithoutInitializing("row_count") , node_count ) // will deep_copy to 0 inside loop
			, row_map( "graph_row_map" , node_count + 1 )
			, node_node_set()
			, phase( FILL_NODE_SET )
			, graph()
			, elem_graph()
			{
			//--------------------------------
			// Guess at capacity required for the map:

			Kokkos::Timer wall_clock ;

			wall_clock.reset();
			phase = FILL_NODE_SET ;

			// upper bound on the capacity
			size_t set_capacity = (28ull * node_count) / 2;
			unsigned failed_insert_count = 0 ;

			do {
			// Zero the row count to restart the fill
			Kokkos::deep_copy( row_count , 0u );

			node_node_set = SetType( ( set_capacity += failed_insert_count ) );

			// May be larger that requested:
			set_capacity = node_node_set.capacity();

			Kokkos::parallel_reduce( Kokkos::RangePolicy<execution_space,TagFillNodeSet>(0,elem_node_id.dimension_0())
			, *this
			, failed_insert_count );

			} while ( failed_insert_count );

			execution_space::fence();
			results.ratio = (double)node_node_set.size() / (double)node_node_set.capacity();
			results.fill_node_set = wall_clock.seconds();
			//--------------------------------

			wall_clock.reset();
			phase = SCAN_NODE_COUNT ;

			// Exclusive scan of row_count into row_map
			// including the final total in the 'node_count + 1' position.
			// Zero the 'row_count' values.
			Kokkos::parallel_scan( node_count , *this );

			// Zero the row count for the fill:
			Kokkos::deep_copy( row_count , 0u );

			unsigned graph_entry_count = 0 ;

			Kokkos::deep_copy( graph_entry_count , row_total );

			// Assign graph's row_map and allocate graph's entries
			graph.row_map = row_map ;
			graph.entries = typename CrsGraphType::entries_type( "graph_entries" , graph_entry_count );

			//--------------------------------
			// Fill graph's entries from the (node,node) set.

			execution_space::fence();
			results.scan_node_count = wall_clock.seconds();

			wall_clock.reset();
			phase = FILL_GRAPH_ENTRIES ;
			Kokkos::parallel_for( node_node_set.capacity() , *this );

			execution_space::fence();
			results.fill_graph_entries = wall_clock.seconds();

			//--------------------------------
			// Done with the temporary sets and arrays
			wall_clock.reset();
			phase = SORT_GRAPH_ENTRIES ;

			row_total = UnsignedValue();
			row_count = RowMapType();
			row_map = RowMapType();
			node_node_set.clear();

			//--------------------------------

			Kokkos::parallel_for( node_count , *this );

			execution_space::fence();
			results.sort_graph_entries = wall_clock.seconds();

			//--------------------------------
			// Element-to-graph mapping:
			wall_clock.reset();
			phase = FILL_ELEMENT_GRAPH ;
			elem_graph = ElemGraphType("elem_graph", elem_node_id.dimension_0() );
			Kokkos::parallel_for( elem_node_id.dimension_0() , *this );

			execution_space::fence();
			results.fill_element_graph = wall_clock.seconds();
			}

			//------------------------------------
			// parallel_for: create map and count row length

			KOKKOS_INLINE_FUNCTION
			void operator()( const TagFillNodeSet & , unsigned ielem , unsigned & count ) const
			{
			// Loop over element's (row_local_node,col_local_node) pairs:
			for ( unsigned row_local_node = 0 ; row_local_node < elem_node_id.dimension_1() ; ++row_local_node ) {

			const unsigned row_node = elem_node_id( ielem , row_local_node );

			for ( unsigned col_local_node = row_local_node ; col_local_node < elem_node_id.dimension_1() ; ++col_local_node ) {

			const unsigned col_node = elem_node_id( ielem , col_local_node );

			// If either node is locally owned then insert the pair into the unordered map:

			if ( row_node < row_count.dimension_0() \|\| col_node < row_count.dimension_0() ) {

			const key_type key = (row_node < col_node) ? make_pair( row_node, col_node ) : make_pair( col_node, row_node ) ;

			const typename SetType::insert_result result = node_node_set.insert( key );

			// A successfull insert: the first time this pair was added
			if ( result.success() ) {

			// If row node is owned then increment count
			if ( row_node < row_count.dimension_0() ) { atomic_fetch_add( & row_count( row_node ) , 1 ); }

			// If column node is owned and not equal to row node then increment count
			if ( col_node < row_count.dimension_0() && col_node != row_node ) { atomic_fetch_add( & row_count( col_node ) , 1 ); }
			}
			else if ( result.failed() ) {
			++count ;
			}
			}
			}
			}
			}

			KOKKOS_INLINE_FUNCTION
			void fill_graph_entries( const unsigned iset ) const
			{
			if ( node_node_set.valid_at(iset) ) {
			// Add each entry to the graph entries.

			const key_type key = node_node_set.key_at(iset) ;
			const unsigned row_node = key.first ;
			const unsigned col_node = key.second ;

			if ( row_node < row_count.dimension_0() ) {
			const unsigned offset = graph.row_map( row_node ) + atomic_fetch_add( & row_count( row_node ) , 1 );
			graph.entries( offset ) = col_node ;
			}

			if ( col_node < row_count.dimension_0() && col_node != row_node ) {
			const unsigned offset = graph.row_map( col_node ) + atomic_fetch_add( & row_count( col_node ) , 1 );
			graph.entries( offset ) = row_node ;
			}
			}
			}

			KOKKOS_INLINE_FUNCTION
			void sort_graph_entries( const unsigned irow ) const
			{
			const unsigned row_beg = graph.row_map( irow );
			const unsigned row_end = graph.row_map( irow + 1 );
			for ( unsigned i = row_beg + 1 ; i < row_end ; ++i ) {
			const unsigned col = graph.entries(i);
			unsigned j = i ;
			for ( ; row_beg < j && col < graph.entries(j-1) ; --j ) {
			graph.entries(j) = graph.entries(j-1);
			}
			graph.entries(j) = col ;
			}
			}

			KOKKOS_INLINE_FUNCTION
			void fill_elem_graph_map( const unsigned ielem ) const
			{
			for ( unsigned row_local_node = 0 ; row_local_node < elem_node_id.dimension_1() ; ++row_local_node ) {

			const unsigned row_node = elem_node_id( ielem , row_local_node );

			for ( unsigned col_local_node = 0 ; col_local_node < elem_node_id.dimension_1() ; ++col_local_node ) {

			const unsigned col_node = elem_node_id( ielem , col_local_node );

			unsigned entry = ~0u ;

			if ( row_node + 1 < graph.row_map.dimension_0() ) {

			const unsigned entry_end = graph.row_map( row_node + 1 );

			entry = graph.row_map( row_node );

			for ( ; entry < entry_end && graph.entries(entry) != col_node ; ++entry );

			if ( entry == entry_end ) entry = ~0u ;
			}

			elem_graph( ielem , row_local_node , col_local_node ) = entry ;
			}
			}
			}

			KOKKOS_INLINE_FUNCTION
			void operator()( const unsigned iwork ) const
			{
			/*
			if ( phase == FILL_NODE_SET ) {
			operator()( TagFillNodeSet() , iwork );
			}
			else */
			if ( phase == FILL_GRAPH_ENTRIES ) {
			fill_graph_entries( iwork );
			}
			else if ( phase == SORT_GRAPH_ENTRIES ) {
			sort_graph_entries( iwork );
			}
			else if ( phase == FILL_ELEMENT_GRAPH ) {
			fill_elem_graph_map( iwork );
			}
			}

			//------------------------------------
			// parallel_scan: row offsets

			typedef unsigned value_type ;

			KOKKOS_INLINE_FUNCTION
			void operator()( const unsigned irow , unsigned & update , const bool final ) const
			{
			// exclusive scan
			if ( final ) { row_map( irow ) = update ; }

			update += row_count( irow );

			if ( final ) {
			if ( irow + 1 == row_count.dimension_0() ) {
			row_map( irow + 1 ) = update ;
			row_total() = update ;
			}
			}
			}

			// For the reduce phase:
			KOKKOS_INLINE_FUNCTION
			void init( const TagFillNodeSet & , unsigned & update ) const { update = 0 ; }

			KOKKOS_INLINE_FUNCTION
			void join( const TagFillNodeSet &
			, volatile unsigned & update
			, volatile const unsigned & input ) const { update += input ; }

			// For the scan phase::
			KOKKOS_INLINE_FUNCTION
			void init( unsigned & update ) const { update = 0 ; }

			KOKKOS_INLINE_FUNCTION
			void join( volatile unsigned & update
			, volatile const unsigned & input ) const { update += input ; }

			//------------------------------------
			};

			} /* namespace FENL */
			} /* namespace Example */
			} /* namespace Kokkos */

			//----------------------------------------------------------------------------

			namespace Kokkos {
			namespace Example {
			namespace FENL {

			template< class ElemCompType >
			class NodeElemGatherFill {
			public:

			typedef typename ElemCompType::execution_space execution_space ;
			typedef typename ElemCompType::vector_type vector_type ;
			typedef typename ElemCompType::sparse_matrix_type sparse_matrix_type ;
			typedef typename ElemCompType::elem_node_type elem_node_type ;
			typedef typename ElemCompType::elem_vectors_type elem_vectors_type ;
			typedef typename ElemCompType::elem_matrices_type elem_matrices_type ;
			typedef typename ElemCompType::elem_graph_type elem_graph_type ;

			static const unsigned ElemNodeCount = ElemCompType::ElemNodeCount ;

			//------------------------------------

			private:

			typedef Kokkos::StaticCrsGraph< unsigned[2] , execution_space > CrsGraphType ;
			typedef typename CrsGraphType::row_map_type::non_const_type RowMapType ;
			typedef Kokkos::View< unsigned , execution_space > UnsignedValue ;

			enum PhaseType { FILL_NODE_COUNT ,
			SCAN_NODE_COUNT ,
			FILL_GRAPH_ENTRIES ,
			SORT_GRAPH_ENTRIES ,
			GATHER_FILL };

			const elem_node_type elem_node_id ;
			const elem_graph_type elem_graph ;
			UnsignedValue row_total ;
			RowMapType row_count ;
			RowMapType row_map ;
			CrsGraphType graph ;
			vector_type residual ;
			sparse_matrix_type jacobian ;
			elem_vectors_type elem_residual ;
			elem_matrices_type elem_jacobian ;
			PhaseType phase ;

			public:

			NodeElemGatherFill()
			: elem_node_id()
			, elem_graph()
			, row_total()
			, row_count()
			, row_map()
			, graph()
			, residual()
			, jacobian()
			, elem_residual()
			, elem_jacobian()
			, phase( FILL_NODE_COUNT )
			{}

			NodeElemGatherFill( const NodeElemGatherFill & rhs )
			: elem_node_id( rhs.elem_node_id )
			, elem_graph( rhs.elem_graph )
			, row_total( rhs.row_total )
			, row_count( rhs.row_count )
			, row_map( rhs.row_map )
			, graph( rhs.graph )
			, residual( rhs.residual )
			, jacobian( rhs.jacobian )
			, elem_residual( rhs.elem_residual )
			, elem_jacobian( rhs.elem_jacobian )
			, phase( rhs.phase )
			{}

			NodeElemGatherFill( const elem_node_type & arg_elem_node_id ,
			const elem_graph_type & arg_elem_graph ,
			const vector_type & arg_residual ,
			const sparse_matrix_type & arg_jacobian ,
			const elem_vectors_type & arg_elem_residual ,
			const elem_matrices_type & arg_elem_jacobian )
			: elem_node_id( arg_elem_node_id )
			, elem_graph( arg_elem_graph )
			, row_total( "row_total" )
			, row_count( "row_count" , arg_residual.dimension_0() )
			, row_map( "graph_row_map" , arg_residual.dimension_0() + 1 )
			, graph()
			, residual( arg_residual )
			, jacobian( arg_jacobian )
			, elem_residual( arg_elem_residual )
			, elem_jacobian( arg_elem_jacobian )
			, phase( FILL_NODE_COUNT )
			{
			//--------------------------------
			// Count node->element relations

			phase = FILL_NODE_COUNT ;

			Kokkos::parallel_for( elem_node_id.dimension_0() , *this );

			//--------------------------------

			phase = SCAN_NODE_COUNT ;

			// Exclusive scan of row_count into row_map
			// including the final total in the 'node_count + 1' position.
			// Zero the 'row_count' values.
			Kokkos::parallel_scan( residual.dimension_0() , *this );

			// Zero the row count for the fill:
			Kokkos::deep_copy( row_count , typename RowMapType::value_type(0) );

			unsigned graph_entry_count = 0 ;

			Kokkos::deep_copy( graph_entry_count , row_total );

			// Assign graph's row_map and allocate graph's entries
			graph.row_map = row_map ;

			typedef typename CrsGraphType::entries_type graph_entries_type ;

			graph.entries = graph_entries_type( "graph_entries" , graph_entry_count );

			//--------------------------------
			// Fill graph's entries from the (node,node) set.

			phase = FILL_GRAPH_ENTRIES ;

			Kokkos::deep_copy( row_count , 0u );
			Kokkos::parallel_for( elem_node_id.dimension_0() , *this );

			execution_space::fence();

			//--------------------------------
			// Done with the temporary sets and arrays

			row_total = UnsignedValue();
			row_count = RowMapType();
			row_map = RowMapType();

			//--------------------------------

			phase = SORT_GRAPH_ENTRIES ;
			Kokkos::parallel_for( residual.dimension_0() , *this );

			execution_space::fence();

			phase = GATHER_FILL ;
			}

			void apply() const
			{
			Kokkos::parallel_for( residual.dimension_0() , *this );
			}

			//------------------------------------
			//------------------------------------
			// parallel_for: Count node->element pairs

			KOKKOS_INLINE_FUNCTION
			void fill_node_count( const unsigned ielem ) const
			{
			for ( unsigned row_local_node = 0 ; row_local_node < elem_node_id.dimension_1() ; ++row_local_node ) {

			const unsigned row_node = elem_node_id( ielem , row_local_node );

			if ( row_node < row_count.dimension_0() ) {
			atomic_fetch_add( & row_count( row_node ) , 1 );
			}
			}
			}

			KOKKOS_INLINE_FUNCTION
			void fill_graph_entries( const unsigned ielem ) const
			{
			for ( unsigned row_local_node = 0 ; row_local_node < elem_node_id.dimension_1() ; ++row_local_node ) {

			const unsigned row_node = elem_node_id( ielem , row_local_node );

			if ( row_node < row_count.dimension_0() ) {

			const unsigned offset = graph.row_map( row_node ) + atomic_fetch_add( & row_count( row_node ) , 1 );

			graph.entries( offset , 0 ) = ielem ;
			graph.entries( offset , 1 ) = row_local_node ;
			}
			}
			}

			KOKKOS_INLINE_FUNCTION
			void sort_graph_entries( const unsigned irow ) const
			{
			const unsigned row_beg = graph.row_map( irow );
			const unsigned row_end = graph.row_map( irow + 1 );
			for ( unsigned i = row_beg + 1 ; i < row_end ; ++i ) {
			const unsigned elem = graph.entries(i,0);
			const unsigned local = graph.entries(i,1);
			unsigned j = i ;
			for ( ; row_beg < j && elem < graph.entries(j-1,0) ; --j ) {
			graph.entries(j,0) = graph.entries(j-1,0);
			graph.entries(j,1) = graph.entries(j-1,1);
			}
			graph.entries(j,0) = elem ;
			graph.entries(j,1) = local ;
			}
			}

			//------------------------------------

			KOKKOS_INLINE_FUNCTION
			void gather_fill( const unsigned irow ) const
			{
			const unsigned node_elem_begin = graph.row_map(irow);
			const unsigned node_elem_end = graph.row_map(irow+1);

			// for each element that a node belongs to

			for ( unsigned i = node_elem_begin ; i < node_elem_end ; i++ ) {

			const unsigned elem_id = graph.entries( i, 0);
			const unsigned row_index = graph.entries( i, 1);

			residual(irow) += elem_residual(elem_id, row_index);

			// for each node in a particular related element
			// gather the contents of the element stiffness
			// matrix that belong in irow

			for ( unsigned j = 0 ; j < ElemNodeCount ; ++j ) {
			const unsigned A_index = elem_graph( elem_id , row_index , j );

			jacobian.coeff( A_index ) += elem_jacobian( elem_id, row_index, j );
			}
			}
			}

			//------------------------------------

			KOKKOS_INLINE_FUNCTION
			void operator()( const unsigned iwork ) const
			{
			if ( phase == FILL_NODE_COUNT ) {
			fill_node_count( iwork );
			}
			else if ( phase == FILL_GRAPH_ENTRIES ) {
			fill_graph_entries( iwork );
			}
			else if ( phase == SORT_GRAPH_ENTRIES ) {
			sort_graph_entries( iwork );
			}
			else if ( phase == GATHER_FILL ) {
			gather_fill( iwork );
			}
			}

			//------------------------------------
			// parallel_scan: row offsets

			typedef unsigned value_type ;

			KOKKOS_INLINE_FUNCTION
			void operator()( const unsigned irow , unsigned & update , const bool final ) const
			{
			// exclusive scan
			if ( final ) { row_map( irow ) = update ; }

			update += row_count( irow );

			if ( final ) {
			if ( irow + 1 == row_count.dimension_0() ) {
			row_map( irow + 1 ) = update ;
			row_total() = update ;
			}
			}
			}

			KOKKOS_INLINE_FUNCTION
			void init( unsigned & update ) const { update = 0 ; }

			KOKKOS_INLINE_FUNCTION
			void join( volatile unsigned & update , const volatile unsigned & input ) const { update += input ; }
			};

			} /* namespace FENL */
			} /* namespace Example */
			} /* namespace Kokkos */

			//----------------------------------------------------------------------------

			namespace Kokkos {
			namespace Example {
			namespace FENL {

			template< class FiniteElementMeshType , class SparseMatrixType >
			class ElementComputation ;


			template< class ExecSpace , BoxElemPart::ElemOrder Order , class CoordinateMap , typename ScalarType >
			class ElementComputation<
			Kokkos::Example::BoxElemFixture< ExecSpace , Order , CoordinateMap > ,
			Kokkos::Example::CrsMatrix< ScalarType , ExecSpace > >
			{
			public:

			typedef Kokkos::Example::BoxElemFixture< ExecSpace, Order, CoordinateMap > mesh_type ;
			typedef Kokkos::Example::HexElement_Data< mesh_type::ElemNode > element_data_type ;

			typedef Kokkos::Example::CrsMatrix< ScalarType , ExecSpace > sparse_matrix_type ;
			typedef typename sparse_matrix_type::StaticCrsGraphType sparse_graph_type ;

			typedef ExecSpace execution_space ;
			typedef ScalarType scalar_type ;

			static const unsigned SpatialDim = element_data_type::spatial_dimension ;
			static const unsigned TensorDim = SpatialDim * SpatialDim ;
			static const unsigned ElemNodeCount = element_data_type::element_node_count ;
			static const unsigned FunctionCount = element_data_type::function_count ;
			static const unsigned IntegrationCount = element_data_type::integration_count ;

			//------------------------------------

			typedef typename mesh_type::node_coord_type node_coord_type ;
			typedef typename mesh_type::elem_node_type elem_node_type ;
			typedef Kokkos::View< scalar_type*[FunctionCount][FunctionCount] , execution_space > elem_matrices_type ;
			typedef Kokkos::View< scalar_type*[FunctionCount] , execution_space > elem_vectors_type ;
			typedef Kokkos::View< scalar_type* , execution_space > vector_type ;

			typedef typename NodeNodeGraph< elem_node_type , sparse_graph_type , ElemNodeCount >::ElemGraphType elem_graph_type ;

			//------------------------------------


			//------------------------------------
			// Computational data:

			const element_data_type elem_data ;
			const elem_node_type elem_node_ids ;
			const node_coord_type node_coords ;
			const elem_graph_type elem_graph ;
			const elem_matrices_type elem_jacobians ;
			const elem_vectors_type elem_residuals ;
			const vector_type solution ;
			const vector_type residual ;
			const sparse_matrix_type jacobian ;
			const scalar_type coeff_K ;

			ElementComputation( const ElementComputation & rhs )
			: elem_data()
			, elem_node_ids( rhs.elem_node_ids )
			, node_coords( rhs.node_coords )
			, elem_graph( rhs.elem_graph )
			, elem_jacobians( rhs.elem_jacobians )
			, elem_residuals( rhs.elem_residuals )
			, solution( rhs.solution )
			, residual( rhs.residual )
			, jacobian( rhs.jacobian )
			, coeff_K( rhs.coeff_K )
			{}

			// If the element->sparse_matrix graph is provided then perform atomic updates
			// Otherwise fill per-element contributions for subequent gather-add into a residual and jacobian.
			ElementComputation( const mesh_type & arg_mesh ,
			const scalar_type arg_coeff_K ,
			const vector_type & arg_solution ,
			const elem_graph_type & arg_elem_graph ,
			const sparse_matrix_type & arg_jacobian ,
			const vector_type & arg_residual )
			: elem_data()
			, elem_node_ids( arg_mesh.elem_node() )
			, node_coords( arg_mesh.node_coord() )
			, elem_graph( arg_elem_graph )
			, elem_jacobians()
			, elem_residuals()
			, solution( arg_solution )
			, residual( arg_residual )
			, jacobian( arg_jacobian )
			, coeff_K( arg_coeff_K )
			{}

			ElementComputation( const mesh_type & arg_mesh ,
			const scalar_type arg_coeff_K ,
			const vector_type & arg_solution )
			: elem_data()
			, elem_node_ids( arg_mesh.elem_node() )
			, node_coords( arg_mesh.node_coord() )
			, elem_graph()
			, elem_jacobians( "elem_jacobians" , arg_mesh.elem_count() )
			, elem_residuals( "elem_residuals" , arg_mesh.elem_count() )
			, solution( arg_solution )
			, residual()
			, jacobian()
			, coeff_K( arg_coeff_K )
			{}

			//------------------------------------

			void apply() const
			{
			parallel_for( elem_node_ids.dimension_0() , *this );
			}

			//------------------------------------

			static const unsigned FLOPS_transform_gradients =
			/* Jacobian / FunctionCount TensorDim * 2 +
			/* Inverse jacobian / TensorDim 6 + 6 +
			/* Gradient transform / FunctionCount 15 ;

			KOKKOS_INLINE_FUNCTION
			float transform_gradients(
			const float grad[][ FunctionCount ] , // Gradient of bases master element
			const double x[] ,
			const double y[] ,
			const double z[] ,
			float dpsidx[] ,
			float dpsidy[] ,
			float dpsidz[] ) const
			{
			enum { j11 = 0 , j12 = 1 , j13 = 2 ,
			j21 = 3 , j22 = 4 , j23 = 5 ,
			j31 = 6 , j32 = 7 , j33 = 8 };

			// Jacobian accumulation:

			double J[ TensorDim ] = { 0, 0, 0, 0, 0, 0, 0, 0, 0 };

			for( unsigned i = 0; i < FunctionCount ; ++i ) {
			const double x1 = x[i] ;
			const double x2 = y[i] ;
			const double x3 = z[i] ;

			const float g1 = grad[0][i] ;
			const float g2 = grad[1][i] ;
			const float g3 = grad[2][i] ;

			J[j11] += g1 * x1 ;
			J[j12] += g1 * x2 ;
			J[j13] += g1 * x3 ;

			J[j21] += g2 * x1 ;
			J[j22] += g2 * x2 ;
			J[j23] += g2 * x3 ;

			J[j31] += g3 * x1 ;
			J[j32] += g3 * x2 ;
			J[j33] += g3 * x3 ;
			}

			// Inverse jacobian:

			float invJ[ TensorDim ] = {
			static_cast<float>( J[j22] * J[j33] - J[j23] * J[j32] ) ,
			static_cast<float>( J[j13] * J[j32] - J[j12] * J[j33] ) ,
			static_cast<float>( J[j12] * J[j23] - J[j13] * J[j22] ) ,

			static_cast<float>( J[j23] * J[j31] - J[j21] * J[j33] ) ,
			static_cast<float>( J[j11] * J[j33] - J[j13] * J[j31] ) ,
			static_cast<float>( J[j13] * J[j21] - J[j11] * J[j23] ) ,

			static_cast<float>( J[j21] * J[j32] - J[j22] * J[j31] ) ,
			static_cast<float>( J[j12] * J[j31] - J[j11] * J[j32] ) ,
			static_cast<float>( J[j11] * J[j22] - J[j12] * J[j21] ) };

			const float detJ = J[j11] * invJ[j11] +
			J[j21] * invJ[j12] +
			J[j31] * invJ[j13] ;

			const float detJinv = 1.0 / detJ ;

			for ( unsigned i = 0 ; i < TensorDim ; ++i ) { invJ[i] *= detJinv ; }

			// Transform gradients:

			for( unsigned i = 0; i < FunctionCount ; ++i ) {
			const float g0 = grad[0][i];
			const float g1 = grad[1][i];
			const float g2 = grad[2][i];

			dpsidx[i] = g0 * invJ[j11] + g1 * invJ[j12] + g2 * invJ[j13];
			dpsidy[i] = g0 * invJ[j21] + g1 * invJ[j22] + g2 * invJ[j23];
			dpsidz[i] = g0 * invJ[j31] + g1 * invJ[j32] + g2 * invJ[j33];
			}

			return detJ ;
			}

			KOKKOS_INLINE_FUNCTION
			void contributeResidualJacobian(
			const float coeff_k ,
			const double dof_values[] ,
			const float dpsidx[] ,
			const float dpsidy[] ,
			const float dpsidz[] ,
			const float detJ ,
			const float integ_weight ,
			const float bases_vals[] ,
			double elem_res[] ,
			double elem_mat[][ FunctionCount ] ) const
			{
			double value_at_pt = 0 ;
			double gradx_at_pt = 0 ;
			double grady_at_pt = 0 ;
			double gradz_at_pt = 0 ;

			for ( unsigned m = 0 ; m < FunctionCount ; m++ ) {
			value_at_pt += dof_values[m] * bases_vals[m] ;
			gradx_at_pt += dof_values[m] * dpsidx[m] ;
			grady_at_pt += dof_values[m] * dpsidy[m] ;
			gradz_at_pt += dof_values[m] * dpsidz[m] ;
			}

			const scalar_type k_detJ_weight = coeff_k * detJ * integ_weight ;
			const double res_val = value_at_pt * value_at_pt * detJ * integ_weight ;
			const double mat_val = 2.0 * value_at_pt * detJ * integ_weight ;

			// $$ R_i = \int_{\Omega} \nabla \phi_i \cdot (k \nabla T) + \phi_i T^2 d \Omega $$
			// $$ J_{i,j} = \frac{\partial R_i}{\partial T_j} = \int_{\Omega} k \nabla \phi_i \cdot \nabla \phi_j + 2 \phi_i \phi_j T d \Omega $$

			for ( unsigned m = 0; m < FunctionCount; ++m) {
			double * const mat = elem_mat[m] ;
			const float bases_val_m = bases_vals[m];
			const float dpsidx_m = dpsidx[m] ;
			const float dpsidy_m = dpsidy[m] ;
			const float dpsidz_m = dpsidz[m] ;

			elem_res[m] += k_detJ_weight * ( dpsidx_m * gradx_at_pt +
			dpsidy_m * grady_at_pt +
			dpsidz_m * gradz_at_pt ) +
			res_val * bases_val_m ;

			for( unsigned n = 0; n < FunctionCount; n++) {

			mat[n] += k_detJ_weight * ( dpsidx_m * dpsidx[n] +
			dpsidy_m * dpsidy[n] +
			dpsidz_m * dpsidz[n] ) +
			mat_val * bases_val_m * bases_vals[n];
			}
			}
			}

			KOKKOS_INLINE_FUNCTION
			void operator()( const unsigned ielem ) const
			{
			// Gather nodal coordinates and solution vector:

			double x[ FunctionCount ] ;
			double y[ FunctionCount ] ;
			double z[ FunctionCount ] ;
			double val[ FunctionCount ] ;
			unsigned node_index[ ElemNodeCount ];

			for ( unsigned i = 0 ; i < ElemNodeCount ; ++i ) {
			const unsigned ni = elem_node_ids( ielem , i );

			node_index[i] = ni ;

			x[i] = node_coords( ni , 0 );
			y[i] = node_coords( ni , 1 );
			z[i] = node_coords( ni , 2 );

			val[i] = solution( ni );
			}


			double elem_vec[ FunctionCount ] ;
			double elem_mat[ FunctionCount ][ FunctionCount ] ;

			for( unsigned i = 0; i < FunctionCount ; i++ ) {
			elem_vec[i] = 0 ;
			for( unsigned j = 0; j < FunctionCount ; j++){
			elem_mat[i][j] = 0 ;
			}
			}


			for ( unsigned i = 0 ; i < IntegrationCount ; ++i ) {
			float dpsidx[ FunctionCount ] ;
			float dpsidy[ FunctionCount ] ;
			float dpsidz[ FunctionCount ] ;

			const float detJ =
			transform_gradients( elem_data.gradients[i] , x , y , z ,
			dpsidx , dpsidy , dpsidz );

			contributeResidualJacobian( coeff_K ,
			val , dpsidx , dpsidy , dpsidz ,
			detJ ,
			elem_data.weights[i] ,
			elem_data.values[i] ,
			elem_vec , elem_mat );
			}

			#if 0

			if ( 1 == ielem ) {
			printf("ElemResidual { %f %f %f %f %f %f %f %f }\n",
			elem_vec[0], elem_vec[1], elem_vec[2], elem_vec[3],
			elem_vec[4], elem_vec[5], elem_vec[6], elem_vec[7]);

			printf("ElemJacobian {\n");

			for ( unsigned j = 0 ; j < FunctionCount ; ++j ) {
			printf(" { %f %f %f %f %f %f %f %f }\n",
			elem_mat[j][0], elem_mat[j][1], elem_mat[j][2], elem_mat[j][3],
			elem_mat[j][4], elem_mat[j][5], elem_mat[j][6], elem_mat[j][7]);
			}
			printf("}\n");
			}

			#endif

			if ( ! residual.dimension_0() ) {
			for( unsigned i = 0; i < FunctionCount ; i++){
			elem_residuals(ielem, i) = elem_vec[i] ;
			for( unsigned j = 0; j < FunctionCount ; j++){
			elem_jacobians(ielem, i, j) = elem_mat[i][j] ;
			}
			}
			}
			else {
			for( unsigned i = 0 ; i < FunctionCount ; i++ ) {
			const unsigned row = node_index[i] ;
			if ( row < residual.dimension_0() ) {
			atomic_fetch_add( & residual( row ) , elem_vec[i] );

			for( unsigned j = 0 ; j < FunctionCount ; j++ ) {
			const unsigned entry = elem_graph( ielem , i , j );
			if ( entry != ~0u ) {
			atomic_fetch_add( & jacobian.coeff( entry ) , elem_mat[i][j] );
			}
			}
			}
			}
			}
			}
			}; /* ElementComputation */

			//----------------------------------------------------------------------------

			template< class FixtureType , class SparseMatrixType >
			class DirichletComputation ;

			template< class ExecSpace , BoxElemPart::ElemOrder Order , class CoordinateMap , typename ScalarType >
			class DirichletComputation<
			Kokkos::Example::BoxElemFixture< ExecSpace , Order , CoordinateMap > ,
			Kokkos::Example::CrsMatrix< ScalarType , ExecSpace > >
			{
			public:

			typedef Kokkos::Example::BoxElemFixture< ExecSpace, Order, CoordinateMap > mesh_type ;
			typedef typename mesh_type::node_coord_type node_coord_type ;
			typedef typename node_coord_type::value_type scalar_coord_type ;

			typedef Kokkos::Example::CrsMatrix< ScalarType , ExecSpace > sparse_matrix_type ;
			typedef typename sparse_matrix_type::StaticCrsGraphType sparse_graph_type ;

			typedef ExecSpace execution_space ;
			typedef ScalarType scalar_type ;

			//------------------------------------

			typedef Kokkos::View< scalar_type* , execution_space > vector_type ;

			//------------------------------------
			// Computational data:

			const node_coord_type node_coords ;
			const vector_type solution ;
			const sparse_matrix_type jacobian ;
			const vector_type residual ;
			const scalar_type bc_lower_value ;
			const scalar_type bc_upper_value ;
			const scalar_coord_type bc_lower_limit ;
			const scalar_coord_type bc_upper_limit ;
			const unsigned bc_plane ;
			const unsigned node_count ;
			bool init ;


			DirichletComputation( const mesh_type & arg_mesh ,
			const vector_type & arg_solution ,
			const sparse_matrix_type & arg_jacobian ,
			const vector_type & arg_residual ,
			const unsigned arg_bc_plane ,
			const scalar_type arg_bc_lower_value ,
			const scalar_type arg_bc_upper_value )
			: node_coords( arg_mesh.node_coord() )
			, solution( arg_solution )
			, jacobian( arg_jacobian )
			, residual( arg_residual )
			, bc_lower_value( arg_bc_lower_value )
			, bc_upper_value( arg_bc_upper_value )
			, bc_lower_limit( std::numeric_limits<scalar_coord_type>::epsilon() )
			, bc_upper_limit( scalar_coord_type(1) - std::numeric_limits<scalar_coord_type>::epsilon() )
			, bc_plane( arg_bc_plane )
			, node_count( arg_mesh.node_count_owned() )
			, init( false )
			{
			parallel_for( node_count , *this );
			init = true ;
			}

			void apply() const
			{
			parallel_for( node_count , *this );
			}

			//------------------------------------

			KOKKOS_INLINE_FUNCTION
			void operator()( const unsigned inode ) const
			{
			// Apply dirichlet boundary condition on the Solution and Residual vectors.
			// To maintain the symmetry of the original global stiffness matrix,
			// zero out the columns that correspond to boundary conditions, and
			// update the residual vector accordingly

			const unsigned iBeg = jacobian.graph.row_map[inode];
			const unsigned iEnd = jacobian.graph.row_map[inode+1];

			const scalar_coord_type c = node_coords(inode,bc_plane);
			const bool bc_lower = c <= bc_lower_limit ;
			const bool bc_upper = bc_upper_limit <= c ;

			if ( ! init ) {
			solution(inode) = bc_lower ? bc_lower_value : (
			bc_upper ? bc_upper_value : 0 );
			}
			else {
			if ( bc_lower \|\| bc_upper ) {

			residual(inode) = 0 ;

			// zero each value on the row, and leave a one
			// on the diagonal

			for( unsigned i = iBeg ; i < iEnd ; ++i ) {
			jacobian.coeff(i) = int(inode) == int(jacobian.graph.entries(i)) ? 1 : 0 ;
			}
			}
			else {

			// Find any columns that are boundary conditions.
			// Clear them and adjust the residual vector

			for( unsigned i = iBeg ; i < iEnd ; ++i ) {
			const unsigned cnode = jacobian.graph.entries(i) ;
			const scalar_coord_type cc = node_coords(cnode,bc_plane);

			if ( ( cc <= bc_lower_limit ) \|\| ( bc_upper_limit <= cc ) ) {
			jacobian.coeff(i) = 0 ;
			}
			}
			}
			}
			}
			};

			} /* namespace FENL */
			} /* namespace Example */
			} /* namespace Kokkos */

			//----------------------------------------------------------------------------

			/* A Cuda-specific specialization for the element computation functor. */
			#if defined( __CUDACC__ )
			// #include <NonlinearElement_Cuda.hpp>
			#endif

			//----------------------------------------------------------------------------

			#endif /* #ifndef KOKKOS_EXAMPLE_FENLFUNCTORS_HPP */

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lammps/lib/kokkos/example/fenl/fenl_functors.hpp
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